Kenneth got a test of 20 questions. For each correct answer he got 5 points and for each wrong he lost 2 points. Totally Kenneth's scored 72. How many right answers did he give?

Question

We should be using variables for this.

Answer 1

The key here will be to set up a system of 2 equations,

Let x = (Number of correct answers)

and y = (Number of wrong answers)

Since we know the test has 20 questions, we have the following equation

x + y = 20

We can also find the following equation by using his final score and the point value of each write/wrong question.

5(Number of correct answers) - 2(Number of wrong answers) = 72

This can also be written as

5x - 2y = 72

Now we have this system of equations

x + y = 20

5x - 2y = 72

Now we can use the elimination method to solve for x, first multiply the top equation by 2,

2x + 2y = 40

5x - 2y = 72

Add the equations together to get,

7x + 0 = 112

x = 16

Therefore, he got 16 answers right.

Answer 2

72 = 5R - 2W

R=20-W

72 = 5(20-W) - 2W = 100-5W -2W = 100-7W

7W = 100-72

W = 28/7 = 4

R = 20-4 = 16 correct answers